The present invention relates generally to three dimensional (3D) computerized tomography (CT) and more specifically to an improved method and apparatus for acquiring complete projection data for exact image reconstruction of a portion of an object irradiated by a cone beam source.
Conventional CT employs a technique for obtaining cross sectional slices of an object from planar parallel or fan beam irradiation of an entire object. The technique is primarily utilized in medical and industrial diagnostics. Image reconstruction techniques have been predominantly two dimensional. In two dimensions, an undistorted image of an object can be mathematically reconstructed in an exact manner by back projecting a parallel beam which has been attenuated after passing through the object using an inverse transform based on the Fourier Slice Theorem. The use of a parallel beam source and a flat two dimensional detector geometrically simplifies reconstruction but complicates practical considerations having to do with speed and ease of data collection.
Back projections can be mathematically accomplished for a cone beam source by inverse Radon transforming suitable planar integrals. The planar integrals are computed from detector integrals which utilize the measured cone beam projection data i.e. the detected attenuated intensity representative of the density distributions of the object. The use of a cone beam source expedites data acquisition; although when used with a flat detector, complicates geometrical considerations. In the two dimensional case using fan beam geometry, the detector integral are equivalent to the Radon transform of the object. Conventional three dimensional CT imaging typically involves stacking slices representative of the density distribution through the object obtained from various parallel or fan beam attenuation projections. Each projection is associated with a particular view angle or configuration of source and detector relative to the object. A data set is generally acquired by either rotating a source and detector, fixed relative to each other, around an object taking projections as the object is scanned; or alternatively, rotating the object between the fixed source and detector. Unlike the two dimensional case, a direct Radon inversion of three dimensional cone beam data from a cone beam source is not possible. Before the inverse Radon transform can be undertaken, the cone beam detector integrals must be reconfigured into planar integrals suitable for inverse Radon transformation.
This problem was addressed in two commonly assigned patent applications: U.S. patent application Ser. No. 07/631,815 filed Dec. 18, 1990 now U.S. Pat. No. 5,257,183 by Kwok C. Tam entitled METHOD AND APPARATUS FOR CONVERTING CONE BEAM X-RAY PROJECTION DATA TO PLANAR INTEGRAL AND RECONSTRUCTING A THREE-DIMENSIONAL COMPUTERIZED TOMOGRAPHY (CT) IMAGE OF AN OBJECT discloses method and apparatus for converting cone beam data to values representing planar integrals on any arbitrary set of planes in Radon space for 3D image reconstruction through inverse Radon transformation. A related U.S. patent application Ser. No. 07/631,818 filed on Dec. 21, 1990 now abandoned by Kwok C. Tam entitled PARALLEL PROCESSING METHOD AND APPARATUS FOR RECONSTRUCTING THREE-DIMENSIONAL COMPUTERIZED TOMOGRAPHY (CT) IMAGE OF AN OBJECT FROM CONE BEAM PROJECTION DATA OR FROM PLANAR INTEGRALS discloses a two step approach for performing an inverse Radon transform from planar integrals obtained on a plurality of coaxial planes. The first step involves calculating from the planar integrals a two dimensional projection image of the object on each of the coaxial planes; while the second step involves defining normal slices through these coaxial planes from which a two dimensional reconstruction of each slice is obtained. In this slice by slice way, the reconstruction algorithms operate on the plurality of planar integrals to produce a three dimensional image of the object.
It is further essential to note that the acquired data set is complete only if it provides data at every point in Radon space, i.e. Radon space must be sufficiently filled with data over the region of support in Radon space which topologically corresponds to a region of support in the object space. Radon data is typically acquired by exposing the entire object within the field of view of the source. Sufficient filling of Radon space by various scanning configurations is necessary for exact image reconstruction. Furthermore, if the detector integral space is filled over the region of support in Radon space for the object, the data set is complete. Bruce D. Smith in an article entitled "Image Reconstruction from Cone-Beam Projections: Necessary and Sufficient Conditions and Reconstruction Methods," IEEE Trans. Med. Imag., MI-4 (1985) 14, has shown that a cone beam data set is complete if each plane passing through the object cuts the scanning trajectory in at least one point. This criterion assumes that the detector is fixed relative to the source and that the entire object can be scanned within the field of view of the source. Depending on the scanning configuration employed to obtain the cone beam projection data, the data set in Radon space may or may not be complete. Utilizing an incomplete data set in image reconstruction by Radon inversion introduces artifacts which compromise image quality and may render the image inadequate for medical or industrial diagnostic use. A scanning configuration is suggested by Gerald N. Minerbo, "Convolutional Reconstruction from Cone-Beam Projection Data" IEEE Trans. Nucl. Sci., Vol. NS-26, No. 2, pp. 2682-2684 (April 1979); and Heang K. Tuy, "An Inversion Formula for Cone-Beam Reconstruction", SIAM J. Math., Vol. 43, No. 3, pp. 546-552 (June 1983) which Smith in his 1985 article identifies as satisfying the completeness criterion. This scanning configuration comprises two circular trajectories whose axes of rotation are normal with respect to one another. Such a scanning configuration is not practical. Another complete scanning trajectory has been recently disclosed in commonly assigned U.S. patent application Ser. No. 07/572,651, filed Aug. 27, 1990 now U.S. Pat. No. 5,073,910, by Eberhard et al entitled "SQUARE WAVE CONE BEAM SCANNING TRAJECTORY FOR DATA COMPLETENESS IN THREE-DIMENSIONAL COMPUTERIZED TOMOGRAPHY". A scanning configuration which minimizes data incompleteness is disclosed in commonly-assigned U.S. patent application Ser. No. 07/572,590, filed Aug. 27, 1990 now U.S. Pat. No. 5,068,882, by Eberhard entitled "DUAL PARALLEL CONE BEAM CIRCULAR SCANNING TRAJECTORIES FOR REDUCED DATA INCOMPLETENESS IN THREE DIMENSIONAL COMPUTERIZED TOMOGRAPHY". While effective to eliminate or reduce data set incompleteness, each of these approaches adds complexity to the scanning configuration either by requiring scanning in a direction other than about the axis of rotation or by requiring additional source/detector pairs. Accordingly, the scanning geometry most commonly adopted is the circular scanning trajectory which engulfs the entire object in the field of view of the source.
Commonly assigned U.S. patent application Ser. No. 07/572,590 discloses an apriori approach to reducing the effects of incompleteness on three dimensional cone beam reconstruction by correcting two dimensional projection images obtained on each of a plurality of coaxial planes in Radon space using optically obtained object boundary information. From this, a three dimensional image is reconstructed from slices normal to the common axis in a slice by slice manner using two dimensional reconstruction on each slice. This apriori corrective approach is not exact in that it is not an inherently a three dimensional CT reconstruction.